﻿using System.Collections.Generic;

namespace ProblemsSet
{
    public class Problem_103 : BaseProblem
    {
        public override object GetResult()
        {

            var tmp = MathLogic.FormeMinSet(7);
            var res = "";
            foreach (var l in tmp)
            {
                res += l;
            }
            
            return res;
        }

        
        public override string Problem
        {
            get
            {
                return @"Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true:

S(B)  S(C); that is, sums of subsets cannot be equal.
If B contains more elements than C then S(B)  S(C).
If S(A) is minimised for a given n, we shall call it an optimum special sum set. The first five optimum special sum sets are given below.

n = 1: {1}
n = 2: {1, 2}
n = 3: {2, 3, 4}
n = 4: {3, 5, 6, 7}
n = 5: {6, 9, 11, 12, 13}

It seems that for a given optimum set, A = {a1, a2, ... , an}, the next optimum set is of the form B = {b, a1+b, a2+b, ... ,an+b}, where b is the 'middle' element on the previous row.

By applying this 'rule' we would expect the optimum set for n = 6 to be A = {11, 17, 20, 22, 23, 24}, with S(A) = 117. However, this is not the optimum set, as we have merely applied an algorithm to provide a near optimum set. The optimum set for n = 6 is A = {11, 18, 19, 20, 22, 25}, with S(A) = 115 and corresponding set string: 111819202225.

Given that A is an optimum special sum set for n = 7, find its set string.

NOTE: This problem is related to problems 105 and 106.";
            }
        }

        public override bool IsSolved
        {
            get
            {
                return true;
            }
        }

        public override object Answer
        {
            get
            {
                return "20313839404245";
            }
        }

    }
}
